Fearing former Kansas Secretary of State Kris Kobach could win the Republican nomination to succeed retiring Sen. Pat Roberts and put an otherwise red seat in jeopardy, McConnell and other party insiders are desperate for Pompeo to run. But concern about the politically divisive Kobach aside, Republican strategists tend to agree that running for Senate is the better play for Pompeo if his White House ambitions are real, especially if President Trump loses reelection.

For Pompeo, a Senate seat would help him stay relevant heading into the 2024 presidential campaign. He would be in demand for TV and conservative talk radio appearances, allowing him to cultivate grassroots enthusiasm and internet fundraising.

“It keeps him in front of the public,” said David McIntosh, a Republican former congressman who runs the Club for Growth, a conservative group encouraging Pompeo to run for Senate.